CN115270635A - Bayes-neural network high-rise building earthquake demand and vulnerability prediction method - Google Patents
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Abstract
The invention belongs to the field of earthquake demand analysis and structural earthquake resistance evaluation of super high-rise buildings, and provides a Bayesian-neural network high-rise building earthquake demand and vulnerability prediction method. The high-rise building earthquake response rapid prediction model based on the neural network technology can greatly reduce the workload of nonlinear dynamic time-course analysis. For the same type of super high-rise building, the structural response of the structure under the earthquake action can be estimated only by inputting the material characteristics, the structural characteristics and the earthquake motion intensity of the structure. In addition, the influence of material characteristics, structural characteristics and seismic dynamic strength is also considered in the seismic demand model based on the Bayesian theory, and the posterior probability distribution of the unknown parameters of the model provides a feasible way for considering the uncertainty of the demand model. The method for quickly predicting the vulnerability of the earthquake provided by the invention is beneficial to carrying out quick performance evaluation on the high-rise building after the earthquake, and has guiding significance for making maintenance and reinforcement measures of the structure after the earthquake.
Description
Technical Field
The invention belongs to the field of earthquake demand analysis and structural earthquake resistance evaluation of super high-rise buildings, and particularly relates to a high-rise building earthquake demand model and a quick vulnerability prediction method based on a mixed Bayesian theory-neural network technology.
Background
The super high-rise building has the characteristics of long design service life, important social effect and the like, seismic requirements and vulnerability assessment of the super high-rise building are carried out, and the method has important practical significance for guaranteeing the service safety of the super high-rise building. The demand model of the super high-rise building under the action of the earthquake refers to the functional relation between engineering demand parameters such as structure lateral movement and acceleration and earthquake motion intensity indexes such as peak acceleration and spectral acceleration. Liu Jingbo et al describe a performance-based seismic vulnerability analysis of a square steel tube concrete frame structure in which a seismic demand model and vulnerability point estimates for an engineering structure are typically obtained by: firstly, establishing a finite element model of an engineering structure, carrying out nonlinear dynamic time-course analysis under the action of seismic oscillation, and recording dynamic response parameters (such as top acceleration of a high-rise building and displacement of each layer of the high-rise building) of the structure. The structural response parameter is also called an Engineering Demand Parameter (EDP) of the structure, and the engineering demand parameter and the seismic intensity Index (IM) follow a linear relationship in a logarithmic coordinate system, i.e. the seismic demand model can be expressed as,
ln(EDP)＝θ 1 +θ 2 ln(IM) (1)
second, the seismic vulnerability is defined as: the conditional probability that a structural response reaches or exceeds a given limit state given seismic oscillation intensity, wherein the limit state equation is written,
g(IM|θ)＝ln(C)-ln(EDP) (2)
in the formula, symbol C represents structural ability or resistance.
Third, after the seismic demand model is determined, the seismic vulnerability can be determined by its definition, i.e.
F(IM|θ)＝P[g(IM)≤0|IM] (3)
The traditional method for analyzing the earthquake demand and the vulnerability of the high-rise building (the specific steps refer to the first step to the third step), a large amount of nonlinear power time-course analysis needs to be carried out on the high-rise building. The analysis method has the advantages of clear concept, strong operability and the like, but the method needs heavy calculation workload, and the analysis result is only suitable for a given high-rise building and is inconvenient for engineering application. In addition, the uncertainty of the traditional seismic vulnerability analysis method (the specific steps refer to the first step to the third step) related to the material characteristics, the structural characteristics and the input seismic motion can be considered through a random sampling method, but the cognitive uncertainty hidden in a demand model is usually ignored, and the defect can greatly increase the discreteness of the seismic performance evaluation result of the high-rise building. Therefore, a need exists for a rapid prediction method of an earthquake demand model and vulnerability analysis for super high-rise buildings, and the defects that the traditional analysis method is low in calculation efficiency and cannot comprehensively consider multiple uncertainties are overcome.
Disclosure of Invention
The technical problem to be solved by the invention is two-sided: firstly, reducing the workload of nonlinear power time course analysis by a neural network technology; secondly, a seismic vulnerability analysis method capable of considering multiple uncertainties is provided based on Bayesian theory.
The technical scheme of the invention is as follows:
a Bayesian-neural network high-rise building earthquake demand and vulnerability prediction method comprises the following steps:
step 2, selecting material characteristic parameters: the concrete material comprises the following components in percentage by weight: taking the structure damping ratio, the natural vibration period, the number of layers, the layer height and the structure type as random variables, and extracting random variable samples, wherein the random variable sample amount is 5-10 times of the random variable amount;
step 3, establishing a structure numerical simulation analysis model for evaluating the earthquake vulnerability according to the random variable sample, namely a finite element model of the structure;
step 4, carrying out nonlinear power time-course analysis on a finite element model of the structure under the action of earthquake motion, and recording structure response, including displacement response, acceleration response and stress-strain response of beam-column nodes of the structure;
step 5, describing the mapping relation between the structural response and the random variable under the earthquake action based on a neural network technology by taking the earthquake motion intensity index and the random variable sample selected in the step 2 as an input layer variable and the structural response in the step 4 as an output layer variable; the number of input layer neurons in the neural network is equal to the number of random variables in the input layer, the number of output layer neurons in the neural network is equal to the number of output layer variables or the number of structural response types, and the number of hidden layer neurons in the neural network is expressed by a relational expression: 2, initially determining the number of neurons in an input layer plus 1, and increasing or decreasing the training effect by combining the neural network; in addition, transfer functions in a hidden layer and an output layer need to be determined when a neural network algorithm is written, the transfer functions are selected from a unipolar function logsig, a linear function purelin and a tansig function or are selected according to specific problems, a gradient descent method is adopted to train the neural network, and the training times, the learning rate and the tolerance are 1000, 0.01 and 1e-5; the mapping relation is used for predicting the structural response of the super high-rise building with different material characteristics and structural characteristics under the action of earthquake with different intensities, so that a neural network-based high-rise building earthquake response rapid prediction model is established;
step 6, establishing a physical mechanism-based earthquake demand model based on Bayes updating criterion on the basis of structural response, and determining a posterior probability density function of demand model parameters as shown in formula (4);
where γ is the model error correction term, h i Representing regularization variables influencing the seismic response of the structure, including the elastic modulus of the material, the post-yield stiffness ratio and the damping ratio of the steel; n is a radical of h Is the number of variables in the error correction term; model unknown parameter theta = (theta) 1 ,θ 2 ,θ h1 ,θ h2 ,···,θ hi σ); sigma epsilon represents the error of the model, and the normal distribution with the mean value of 0 and the standard deviation of sigma is obeyed; the posterior probability density function f (theta) of the unknown parameter theta of the model is as follows according to the Bayes updating rule,
f(Θ)＝cL(Θ)p(Θ) (5)
wherein c = [ [ loop factor L (theta) p (theta) d theta] -1 The normalization factor is expressed to ensure that the integral of f (Θ) is 1.0; l (Θ) = uf (Data | Θ) is a likelihood function, and f (Data | Θ) represents a probability density function of an observed value under a given model parameter condition; p (theta) is a prior probability density function of theta, and the prior probability density function without information is p (theta) = 1/sigma;
step 7, obtaining the seismic vulnerability considering multiple uncertainties through a total probability theory, namely
F(IM)＝∫F(IM|θ)f(Θ)dΘ (6)。
The invention has the beneficial effects that: the high-rise building earthquake response rapid prediction model based on the neural network technology can greatly reduce the workload of nonlinear power time-course analysis. For the same type of super high-rise building, the structural response of the structure under the earthquake action can be estimated only by inputting the material characteristics, the structural characteristics and the earthquake motion intensity of the structure. In addition, the influence of material characteristics, structural characteristics and seismic dynamic strength is also considered in the seismic demand model based on the Bayesian theory, and the posterior probability distribution of the unknown parameters of the model provides a feasible way for considering the uncertainty of the demand model. The method for quickly predicting the vulnerability to earthquakes is beneficial to quickly evaluating the performance of high-rise buildings after the earthquakes and has guiding significance for making maintenance and reinforcement measures of structures after the earthquakes.
Drawings
FIG. 1 is a schematic diagram of a structural response rapid prediction model based on neural network technology;
FIG. 2 is a plan view and a three-dimensional structural schematic of a super high-rise building in which the embodiments are used; (a) is a floor plan; (b) is a three-dimensional view;
FIG. 3 is a representation of the prediction results of a structural response prediction model based on neural network technology;
FIG. 4 is a vulnerability curve display determined by a high-rise building earthquake vulnerability rapid prediction method based on a hybrid Bayesian-neural network.
Detailed Description
In order to show the objects, technical solutions and advantages of the present invention more clearly, the technical solutions in the implementation process of the present invention will be described clearly and completely in conjunction with specific super high-rise building cases. Based on the super high-rise building case of the present invention, all other achievements obtained by those skilled in the art without creative efforts belong to the protection scope of the present invention.
A Bayesian-neural network high-rise building earthquake demand and vulnerability prediction method comprises the following steps:
step 2, selecting main material characteristic parameters such as yield strength of steel, strain corresponding to the yield strength, ultimate strength, strain corresponding to the ultimate strength, elastic modulus, post-yield rigidity ratio, compressive strength, strain, tensile strength, elastic modulus and the like of a concrete material, and structural characteristic parameters such as structural damping ratio, natural vibration period, layer number, layer height, structural type and the like as random variables, and extracting corresponding random variable samples, wherein the sample amount of the random variables is 5-10 times of the number of the random variables;
and 3, establishing a structural numerical simulation analysis model for evaluating the earthquake vulnerability, namely a finite element model of the structure according to the random variable sample. One of ordinary skill in the art may choose any commercial or open source finite element analysis platform to build a finite element model of the structure and to perform nonlinear dynamic time course analysis. If the ABAQUS commercial finite element software is adopted to carry out the nonlinear power time course analysis, the structural finite element model can be established by referring to a help document of the ABAQUS, wherein a Command is input in an ABAQUS Command window (DOS window): abaqus doc can obtain help documents. If an OpenSEES open source platform is adopted to carry out nonlinear time course analysis, the user manual can be referred to for relevant work, and details are as follows: https:// opentees. Berkeley. Edu/wiki/index. Php/Getting _ Started.
Step 4, carrying out nonlinear power time-course analysis on the finite element model of the structure under the action of earthquake motion, and recording displacement response, acceleration response, stress-strain response of key parts such as beam-column nodes and the like of the structure;
step 5, using the earthquake dynamic intensity index and the random variable sample selected in the step 2 as input layer variables, using the structural response of the step 4 as output layer variables, and describing the mapping relation between the structural response and the random variables under the earthquake action based on a neural network technology, wherein the number of neurons in the input layer in the neural network is equal to the number of the random variables in the input layer, the number of neurons in the output layer is equal to the number of the variables in the output layer or the number of structural response types, and the number of neurons in the hidden layer can be represented by a relational expression: 2, initially determining the number of neurons in an input layer plus 1, and properly increasing or decreasing the training effect by combining with the neural network; in addition, transfer functions in a hidden layer and an output layer need to be determined when a neural network algorithm is written, the transfer functions are used for increasing the nonlinear characteristics between input information and output information, unipolar functions logsig, linear functions purelin and tansig functions can be selected for the transfer functions of the seismic response prediction problem of the super high-rise building or selected according to specific problems, a gradient descent method is adopted to train the neural network, and the training times, the learning rate and the tolerance are 1000, 0.01 and 1e-5; the invention only gives the suggested value of the network parameter, but not a fixed value, and the ordinary technical personnel in the field can select the proper network parameter according to the concrete engineering problem so as to lead the network to have the best training effect. The mapping relation can be used for predicting the structural response of the super high-rise building with different material characteristics and structural characteristics under the action of earthquake with different intensities, so that a high-rise building earthquake response rapid prediction model based on a neural network is established, as shown in figure 1;
step 6, establishing a physical mechanism-based earthquake demand model based on Bayes updating criterion on the basis of structural response, and determining a posterior probability density function of demand model parameters as shown in formula (4);
where γ is the model error correction term, h i Representing regularization variables affecting the seismic response of the structure, such as material elastic modulus, post-yield stiffness ratio and damping ratio of steel; n is a radical of h Is the number of variables in the error correction term; model unknown parameter theta = (theta) 1 ,θ 2 ,θ h1 ,θ h2 ,···,θ hi σ); sigma epsilon represents the model error, and obeys normal distribution with the mean value of 0 and the standard deviation of sigma; updating the criterion by Bayes, model unknown parameter thetaThe posterior probability density function f (Θ) of (a) is,
f(Θ)＝cL(Θ)p(Θ) (5)
wherein, c = [ [ loop factor L (theta) p (theta) d theta [ ]] -1 The normalization factor is expressed to ensure that the integral of f (Θ) is 1.0; l (Θ) = uf (Data | Θ) is a likelihood function, and f (Data | Θ) represents a probability density function of an observed value under a given model parameter condition; p (theta) is a prior probability density function of theta, and the prior probability density function without information is p (theta) = 1/sigma;
step 7, obtaining the seismic vulnerability considering multiple uncertainties through a total probability theory, namely
F(IM)＝∫F(IM|θ)f(Θ)dΘ (6)。
Examples
A Bayesian-neural network high-rise building earthquake demand and vulnerability prediction method comprises the following steps:
step 2, taking a 42-layer steel frame-RC core tube building as an analysis case, wherein the frame columns of the steel frame are round steel pipe columns, the steel beams are I-shaped steel beams, and the material strength is Q345B; the concrete strength of the RC core tube is C40-C60. The length and width of the cross section of the super high-rise building are 32.4m and 30.6m respectively, see fig. 2 (a); the total height of the building is 152.1m, wherein the height of the first floor is 4.5m, and the heights of other floors are all 3.6m. Selecting the elastic modulus, the yield strength, the post-yield stiffness ratio and the damping ratio of the Q345B steel as random variables, extracting 20 groups of random variable samples, and summarizing the samples in a table 1;
TABLE 1 random variable samples
Step 3, establishing 20 groups of refined finite element models of the super high-rise building cases, as shown in fig. 2 (b);
step 4, randomly dividing the selected 100 earthquake motion records into 20 groups, namely each group comprises 5 earthquake motion time-course curves, randomly matching the earthquake motion time-course curves with 20 structural finite element model samples to form 20 groups of finite element models-earthquake motion records, carrying out nonlinear power time-course analysis, and recording interlayer displacement response of the structure as an engineering requirement parameter index;
step 5, taking the PGA, the elastic modulus, the yield strength, the post-yield stiffness ratio and the damping ratio as input layer variables of the neural network, taking the interlayer displacement response of the structure as output layer variables, and establishing a prediction model of the interlayer lateral displacement response of the structure under the action of the earthquake based on the neural network technology, wherein the prediction result is shown in FIG. 3;
step 6, establishing a seismic demand model based on a physical mechanism based on a Bayes updating criterion, and determining a posterior probability density function of demand model parameters, wherein the influence of elastic modulus, yield strength, post-yield rigidity ratio and damping ratio on the demand model is considered in an error correction term;
and 7, acquiring the seismic vulnerability which can consider multiple uncertainties through a total probability theory, wherein the analysis result is shown in FIG. 4.
Finally, it is to be noted that: the above embodiments are only used to illustrate the technical solution and implementation process of the present invention, and not to limit the same. Those of ordinary skill in the art will understand that: the technical solutions described in the embodiments can be modified, or some technical features can be replaced by equivalents, without departing from the spirit and scope of the technical solutions of the embodiments.
Claims (1)
1. A Bayesian-neural network high-rise building earthquake demand and vulnerability prediction method is characterized by comprising the following steps:
step 1, based on building earthquake-resistant design specifications, determining the type, grouping and earthquake fortification level characteristics of a site where an engineering structure is located by a design file of the engineering structure, and determining a target reaction spectrum curve according to a method provided in the building earthquake-resistant design specifications after obtaining the three characteristics; acquiring an actual measurement seismic oscillation record according to the target reaction spectrum curve;
step 2, selecting material characteristic parameters: the concrete material comprises the following components in percentage by weight: the structure damping ratio, the natural vibration period, the layer number, the layer height and the structure type are used as random variables; extracting random variable samples, wherein the amount of the random variable samples is 5-10 times of the amount of the random variables;
step 3, establishing a structure numerical simulation analysis model for evaluating the earthquake vulnerability, namely a finite element model of the structure, according to the random variable sample;
step 4, carrying out nonlinear power time-course analysis on the finite element model of the structure under the action of earthquake motion, and recording structure response, including displacement response, acceleration response and stress-strain response of beam-column nodes of the structure;
step 5, describing the mapping relation between the structural response and the random variable under the earthquake action based on a neural network technology by taking the earthquake motion intensity index and the random variable sample selected in the step 2 as an input layer variable and the structural response in the step 4 as an output layer variable; the number of input layer neurons in the neural network is equal to the number of random variables in the input layer, the number of output layer neurons in the neural network is equal to the number of output layer variables or the number of structural response types, and the number of hidden layer neurons in the neural network is expressed by a relational expression: 2, initially determining the number of neurons in an input layer plus 1, and increasing or decreasing the training effect by combining the neural network; in addition, transfer functions in a hidden layer and an output layer need to be determined when a neural network algorithm is written, the transfer functions are selected from a unipolar function logsig, a linear function purelin and a tansig function or are selected according to specific problems, a gradient descent method is adopted to train the neural network, and the training times, the learning rate and the tolerance are 1000, 0.01 and 1e-5; the mapping relation is used for predicting the structural response of the super high-rise building with different material characteristics and structural characteristics under the action of earthquake with different intensities, so that a neural network-based high-rise building earthquake response rapid prediction model is established;
step 6, establishing a physical mechanism-based earthquake demand model based on Bayes updating criterion on the basis of structural response, and determining a posterior probability density function of demand model parameters as shown in formula (4);
where gamma is a model error correction term, h i Representing regularization variables influencing the seismic response of the structure, including the elastic modulus of the material, the post-yield stiffness ratio and the damping ratio of the steel; n is a radical of h Is the number of variables in the error correction term; model unknown parameter theta = (theta) 1 ,θ 2 ,θ h1 ,θ h2 ,···,θ hi σ); sigma epsilon represents the model error, and obeys normal distribution with the mean value of 0 and the standard deviation of sigma; the posterior probability density function f (theta) of the unknown parameter theta of the model is as follows according to the Bayes updating rule,
f(Θ)＝cL(Θ)p(Θ) (5)
wherein c = [ [ loop factor L (theta) p (theta) d theta] -1 The normalization factor is expressed to ensure that the integral of f (Θ) is 1.0; l (Θ) = uf (Data | Θ) is a likelihood function, and f (Data | Θ) represents a probability density function of an observed value under a given model parameter condition; p (theta) is a prior probability density function of theta, and the prior probability density function without information is p (theta) = 1/sigma;
step 7, obtaining the seismic vulnerability considering multiple uncertainties through a total probability theory, namely
F(IM)＝∫F(IM|θ)f(Θ)dΘ (6)。
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| CN116882760A (en) * | 2023-08-09 | 2023-10-13 | 北京建筑大学 | Main aftershock risk interval calculation method and system based on Bayesian updating principle |
| CN117494590A (en) * | 2024-01-03 | 2024-02-02 | 国泰新点软件股份有限公司 | Method, device, equipment and storage medium for evaluating earthquake resistance of building facilities |
| CN117574705A (en) * | 2023-11-07 | 2024-02-20 | 哈尔滨工业大学 | RC frame building earthquake time-course response prediction method considering response spectrum constraint |
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| CN117494590A (en) * | 2024-01-03 | 2024-02-02 | 国泰新点软件股份有限公司 | Method, device, equipment and storage medium for evaluating earthquake resistance of building facilities |
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